Unit 1 Lecture Notes

My conclusion from reading this debate for years is to believe that fractional reserve banking cannot emerge on a free market. Beyond the arguments above, I will provide below a synthesis of my views on the topic, particularly as they relate to Bitcoin.

The processing of payments can be understood as a market good that becomes more valuable as the scale of an economy grows, and the circle in which a person trades expands, since there are clear economies of scale for banks in clearing, netting, and settling large numbers of transactions over individuals carrying these out individually. Some examples are paper notes backed by gold, bills of exchange, modern credit cards, and paypal accounts.

In any monetary system, such networks for banking and settlement will emerge, and they will benefit from economies of scale by holding many accounts for people and netting transactions, bypassing the need to physically transfer money (or in the case of Bitcoin, the need to transfer assets on-chain). Under the gold standard, the physical movement of gold was expensive and insecure, and economies of scale accrued to those that physically amassed reserves and thus could provide a centralized clearing mechanism. As a result, only a few global central banks emerged who could cost-effectively trade gold with one another. The emergence of fractional reserve banking on top of this system can then be understood as a result of banks' ability to expand credit, backed by their operational capital and aided by a trusted network of banks with which it can clear.

In a sense, fractional reserve banking could be sustainable when the alternative to dealing with banks is too expensive, and banks' reserves are high enough to make mass withdrawals unlikely. If the physical settlement is expensive and the network of banks is very valuable to its customers, banks could conceivably get away with not keeping all deposits on hand without experiencing a bank run. It is possible for fractional reserve banking to continue in a bank that is the only one in a town, or where it enjoys some monopoly privilege from government, because there are no easy alternatives for clients to process payments if they choose to withdraw their money from the bank. This becomes particularly easy if the money is easy.

The degree to which a bank can get away with fractional reserve banking is a positive function of the cost of final settlement of the monetary asset, and the ease of debasing the monetary asset. Under a gold standard, the cost and time required to move gold around physically is relatively high, so the economies of scale from centralization will provide existing banks a degree of leeway in extending unbacked credit without their depositors noticing or being able to do anything about it. Yet this system is not very sustainable, because the longer it lasts, the safer banks feel, the more risks they take, until it comes crashing down, as was the case during the 19^th century. Since it is not easy to increase the supply of gold on demand, and no lender of last resort is able to print it to bail out banks engaged in fractionally lending gold-backed notes, fractional reserve banking was the bug that kept on derailing the gold standard. Eventually the gold standard itself was sacrificed to keep fractional reserve banking alive, when a dollar based standard was used for settlement. This makes settlement entirely centralized with a government monopoly while leaving the currency elastic to the demands of the banking sector.

Here we see an advantage that bitcoin has over gold: It can provably perform hundreds of thousands of settlements a day, each in under an hour. Compared to the physical movement of gold, the final settlement costs are much lower, which translates to less economies of scale for centralized bitcoin clearing, and thus even less incentive for a central banking ecosystem around Bitcoin to emerge. Any system for bitcoin settlement would be far more distributed at its core than gold. That means a central banking ecosystem around Bitcoin would be far more distributed at its core. The benefits from economies of scale are not as pronounced as with the case of gold. There is room for far more institutions able to perform settlement with one another.

With half a million transactions daily, 1,000 global banks can perform daily final settlement with one another (since the number of transactions would be equal to (n*(n-1)/2). Should we consider settlement on a quarterly basis on average, we would have around 10,000 banks. There are many optimizations to Bitcoin transactions that can be applied, using existing provably working technology that would allow a large increase in transaction capacity by combining multiple outputs in each transaction. As a best case scenario, we could think of 5 million payments per day as being a possible upper limit on on-chain Bitcoin daily payments, and with settlement between each institution and the other happening on average only quarterly, there is scope for having around 27,000 central banks able to settle final transactions on a quarterly basis with one another. This would mean that on average, each 300,000 people would have a central bank able to perform final clearance of payments with any other bank in the world at least once quarterly. With such a large number of banks, most banks will likely not need to settle with one another per quarter, but will have more frequent settlements with closer banks. This is a level of decentralization far beyond what the gold standard could ever afford.

In terms of hardness, Bitcoin's supply growth rate will continue to decline and eventually end up at zero, while gold's supply growth rate is largely constant at around 1-2% as discussed in The Bitcoin Standard; The important distinction here though is that Bitcoin is deterministically and strictly capped, whereas the real gold supply is never really known for certain. One can never really know for sure how much gold there is, and there is no way for easily verifying whether a bank is honest in the holdings it report, except through a very meticulous audit. Given that bitcoin's supply is strictly capped and the coins are always visible on a public ledger, the tracking of bank reserves is less difficult a problem.

The strict cap and transparent supply make it extremely unlikely that fractional reserve banking with Bitcoin will be sustainable. Any entity that engages in it is subject to the threat of bank runs without the safety net of a bail-out from lenders of last resort. Aside from its lower final settlement costs (and thus less incentive for centralization) discussed above, bitcoin is also less susceptible to fractional reserve banking than gold simply because it's much harder to confiscate. But before we discuss the relevance of that, we need to first explain how fractional reserve banking works in the modern financial system.